Toward a Biologically Plausible Model of LGN-V1 Pathways Based on Efficient Coding

Increasing evidence supports the hypothesis that the visual system employs a sparse code to represent visual stimuli, where information is encoded in an efficient way by a small population of cells that respond to sensory input at a given time. This includes simple cells in primary visual cortex (V1), which are defined by their linear spatial integration of visual stimuli. Various models of sparse coding have been proposed to explain physiological phenomena observed in simple cells. However, these models have usually made the simplifying assumption that inputs to simple cells already incorporate linear spatial summation. This overlooks the fact that these inputs are known to have strong non-linearities such the separation of ON and OFF pathways, or separation of excitatory and inhibitory neurons. Consequently these models ignore a range of important experimental phenomena that are related to the emergence of linear spatial summation from non-linear inputs, such as segregation of ON and OFF sub-regions of simple cell receptive fields, the push-pull effect of excitation and inhibition, and phase-reversed cortico-thalamic feedback. Here, we demonstrate that a two-layer model of the visual pathway from the lateral geniculate nucleus to V1 that incorporates these biological constraints on the neural circuits and is based on sparse coding can account for the emergence of these experimental phenomena, diverse shapes of receptive fields and contrast invariance of orientation tuning of simple cells when the model is trained on natural images. The model suggests that sparse coding can be implemented by the V1 simple cells using neural circuits with a simple biologically plausible architecture

Eigenvalue spectral properties of sparse random matrices obeying Dale's law

Understanding the dynamics of large networks of neurons with heterogeneous connectivity architectures is a complex physics problem that demands novel mathematical techniques. Biological neural networks are inherently spatially heterogeneous, making them difficult to mathematically model. Random recurrent neural networks capture complex network connectivity structures and enable mathematically tractability. Our paper generalises previous classical results to sparse connectivity matrices which have distinct excitatory (E) or inhibitory (I) neural populations. By investigating sparse networks we construct our analysis to examine the impacts of all levels of network sparseness, and discover a novel nonlinear interaction between the connectivity matrix and resulting network dynamics, in both the balanced and unbalanced cases. Specifically, we deduce new mathematical dependencies describing the influence of sparsity and distinct E/I distributions on the distribution of eigenvalues (eigenspectrum) of the networked Jacobian. Furthermore, we illustrate that the previous classical results are special cases of the more general results we have described here. Understanding the impacts of sparse connectivities on network dynamics is of particular importance for both theoretical neuroscience and mathematical physics as it pertains to the structure-function relationship of networked systems and their dynamics. Our results are an important step towards developing analysis techniques that are essential to studying the impacts of larger scale network connectivity on network function, and furthering our understanding of brain function and dysfunction.Comment: 18 pages, 6 figure

The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results

Retinal ganglion cells (RGCs) display differences in their morphology and intrinsic electrophysiology. The goal of this study is to characterize the ionic currents that explain the behavior of ON and OFF RGCs and to explore if all morphological types of RGCs exhibit the phenomena described in electrophysiological data. We extend our previous single compartment cell models of ON and OFF RGCs to more biophysically realistic multicompartment cell models and investigate the effect of cell morphology on intrinsic electrophysiological properties. The membrane dynamics are described using the Hodgkin - Huxley type formalism. A subset of published patch-clamp data from isolated intact mouse retina is used to constrain the model and another subset is used to validate the model. Two hundred morphologically distinct ON and OFF RGCs are simulated with various densities of ionic currents in different morphological neuron compartments. Our model predicts that the differences between ON and OFF cells are explained by the presence of the low voltage activated calcium current in OFF cells and absence of such in ON cells. Our study shows through simulation that particular morphological types of RGCs are capable of exhibiting the full range of phenomena described in recent experiments. Comparisons of outputs from different cells indicate that the RGC morphologies that best describe recent experimental results are ones that have a larger ratio of soma to total surface area

An investigation of dendritic delay in octopus cells of the mammalian cochlear nucleus

Octopus cells, located in the mammalian auditory brainstem, receive their excitatory synaptic input exclusively from auditory nerve fibers (ANFs). They respond with accurately timed spikes but are broadly tuned for sound frequency. Since the representation of information in the auditory nerve is well understood, it is possible to pose a number of questions about the relationship between the intrinsic electrophysiology, dendritic morphology, synaptic connectivity, and the ultimate functional role of octopus cells in the brainstem. This study employed a multi-compartmental Hodgkin-Huxley model to determine whether dendritic delay in octopus cells improves synaptic input coincidence detection in octopus cells by compensating for the cochlear traveling wave delay. The propagation time of post-synaptic potentials from synapse to soma was investigated. We found that the total dendritic delay was approximately 0.275 ms. It was observed that low-threshold potassium channels in the dendrites reduce the amplitude dependence of the dendritic delay of post-synaptic potentials. As our hypothesis predicted, the model was most sensitive to acoustic onset events, such as the glottal pulses in speech when the synaptic inputs were arranged such that the model's dendritic delay compensated for the cochlear traveling wave delay across the ANFs. The range of sound frequency input from ANFs was also investigated. The results suggested that input to octopus cells is dominated by high frequency ANFs

Brazing techniques for the fabrication of biocompatible carbon-based electronic devices

Prototype electronic devices have been critical to the discovery and demonstration of the unique properties of new materials, including composites based on carbon nanotubes (CNT) and graphene. However, these devices are not typically constructed with durability or biocompatibility in mind, relying on conductive polymeric adhesives, mechanical clamps or crimps, or solders for electrical connections. In this paper, two key metallization techniques are presented that employ commercially-available brazing alloys to fabricate electronic devices based on diamond and carbonaceous wires. Investigation of the carbon - alloy interfacial interactions was utilized to guide device fabrication. The interplay of both chemical ( adhesive ) and mechanical ( cohesive ) forces at the interface of different forms of carbon was exploited to fabricate either freestanding or substrate-fixed carbonaceous electronic devices. Elemental analysis in conjunction with scanning electron microscopy of the carbon - alloy interface revealed the chemical nature of the Ag alloy bond and the mechanical nature of the Au alloy bond. Electrical characterization revealed the non-rectifying nature of the carbon - Au alloy interconnects. Finally, electronic devices were fabricated, including a Au circuit structure embedded in a polycrystalline diamond substrate